Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0950)

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=3

http://functions.wolfram.com/07.22.03.0950.01

Input Form

HypergeometricPFQ[{-(9/2)}, {3, 9/2}, -z] == (1/(212548976640 z^3)) (4 (2 z (638512875 - 9089406900 z + 46745521200 z^2 + 39547636416 z^3 + 5875755264 z^4 + 259261440 z^5 + 3837952 z^6 + 16384 z^7) BesselJ[0, 2 Sqrt[z]] - Sqrt[z] (1915538625 - 14603141700 z + 31117277520 z^2 + 36820055232 z^3 + 5749408512 z^4 + 257356800 z^5 + 3829760 z^6 + 16384 z^7) BesselJ[1, 2 Sqrt[z]]) + Pi (1915538625 + 12259447200 z - 57210753600 z^2 + 152562009600 z^3 + 152562009600 z^4 + 23247544320 z^5 + 1033224192 z^6 + 15335424 z^7 + 65536 z^8) BesselJ[1, 2 Sqrt[z]] StruveH[0, 2 Sqrt[z]] - Pi (1915538625 + 12259447200 z - 57210753600 z^2 + 152562009600 z^3 + 152562009600 z^4 + 23247544320 z^5 + 1033224192 z^6 + 15335424 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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</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]