Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1270)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=5/2

http://functions.wolfram.com/07.22.03.1270.01

Input Form

HypergeometricPFQ[{-(7/2)}, {5/2, 5/2}, -z] == (1/(409600 z^(3/2))) (2 Sqrt[z] (14385 + 56960 z + 13662 z^2 + 696 z^3 + 8 z^4) Cos[2 Sqrt[z]] + (-1785 + 46620 z + 13010 z^2 + 688 z^3 + 8 z^4) Sin[2 Sqrt[z]] + 8 (-1575 + 15750 z + 31500 z^2 + 7000 z^3 + 350 z^4 + 4 z^5) SinIntegral[2 Sqrt[z]])

Standard Form

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MathML Form

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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]