Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0629)

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=4

http://functions.wolfram.com/07.22.03.0629.01

Input Form

HypergeometricPFQ[{-(11/2)}, {4, 9/2}, z] == (1/(162599967129600 z^3)) (4 (2 z (5934309190425 + 12378112362000 z + 38327163336000 z^2 - 28494499127040 z^3 + 4124307156480 z^4 - 198529634304 z^5 + 3729408000 z^6 - 27590656 z^7 + 65536 z^8) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (10077589766475 + 18153333613800 z + 26953494876000 z^2 - 26590498922880 z^3 + 4028183884800 z^4 - 196688775168 z^5 + 3715670016 z^6 - 27557888 z^7 + 65536 z^8) BesselI[1, 2 Sqrt[z]]) - Pi (5373085843125 + 38686218070500 z + 68775498792000 z^2 + 128380931078400 z^3 - 110040798067200 z^4 + 16302340454400 z^5 - 790416506880 z^6 + 14890106880 z^7 - 110297088 z^8 + 262144 z^9) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (5373085843125 + 38686218070500 z + 68775498792000 z^2 + 128380931078400 z^3 - 110040798067200 z^4 + 16302340454400 z^5 - 790416506880 z^6 + 14890106880 z^7 - 110297088 z^8 + 262144 z^9) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> 128380931078400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 68775498792000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 38686218070500 </cn> <ci> z </ci> </apply> <cn type='integer'> 5373085843125 </cn> </apply> <apply> <ci> BesselI </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> StruveL </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> </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]