Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0644)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=9/2

http://functions.wolfram.com/07.22.03.0644.01

Input Form

HypergeometricPFQ[{-(11/2)}, {9/2, 6}, -z] == (4 (2 Sqrt[z] (-23176013414400 - 110086063718400 z + 206000118064125 z^2 - 159985157270400 z^3 + 229107818459520 z^4 + 113645455515648 z^5 + 11471751019008 z^6 + 405778268160 z^7 + 5833162752 z^8 + 34078720 z^9 + 65536 z^10) BesselJ[0, 2 Sqrt[z]] - (-46352026828800 - 196996114022400 z + 287742163037175 z^2 - 211280649010200 z^3 + 180749203034400 z^4 + 108239873325696 z^5 + 11273814816768 z^6 + 402891208704 z^7 + 5816180736 z^8 + 34045952 z^9 + 65536 z^10) BesselJ[1, 2 Sqrt[z]]) + Pi z^(3/2) (-714620417135625 + 1029053400675300 z - 784040686228800 z^2 + 813079230163200 z^3 + 443497761907200 z^4 + 45486949939200 z^5 + 1617313775616 z^6 + 23298637824 z^7 + 136249344 z^8 + 262144 z^9) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi z^(3/2) (-714620417135625 + 1029053400675300 z - 784040686228800 z^2 + 813079230163200 z^3 + 443497761907200 z^4 + 45486949939200 z^5 + 1617313775616 z^6 + 23298637824 z^7 + 136249344 z^8 + 262144 z^9) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])/(810967336058880 z^(9/2))

Standard Form

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MathML Form

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</mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 9 <sep /> 2 </cn> <cn type='integer'> 6 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 810967336058880 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 262144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 136249344 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]