Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0920)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=2

http://functions.wolfram.com/07.22.03.0920.01

Input Form

HypergeometricPFQ[{-(9/2)}, {2, 9/2}, -z] == (1/(65399685120 z^3)) (4 (2 z (-147349125 - 275051700 z + 11989600560 z^2 + 15420443328 z^3 + 3173587200 z^4 + 179635200 z^5 + 3248128 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (-442047375 - 746568900 z + 6391360080 z^2 + 13976945856 z^3 + 3086537472 z^4 + 178025472 z^5 + 3239936 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]]) + Pi (-442047375 - 943034400 z - 4400827200 z^2 + 35206617600 z^3 + 58677696000 z^4 + 12517908480 z^5 + 715309056 z^6 + 12976128 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (-442047375 - 943034400 z - 4400827200 z^2 + 35206617600 z^3 + 58677696000 z^4 + 12517908480 z^5 + 715309056 z^6 + 12976128 z^7 + 65536 z^8) BesselJ[0, 2 Sqrt[z]] StruveH[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveH </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]