Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0597)

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=5/2

http://functions.wolfram.com/07.22.03.0597.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5/2, 11/2}, z] == (1/(26424115200 z^(9/2))) (-2 Sqrt[z] (343814625 - 261954000 z + 602494200 z^2 + 1722035700 z^3 - 3039891750 z^4 + 594818280 z^5 - 34562040 z^6 + 745384 z^7 - 6152 z^8 + 16 z^9) Cosh[2 Sqrt[z]] + (343814625 + 196465500 z + 130977000 z^2 - 478377900 z^3 + 2594903850 z^4 - 563986080 z^5 + 33849480 z^6 - 739320 z^7 + 6136 z^8 - 16 z^9) Sinh[2 Sqrt[z]] + 32 z^3 (98232750 + 343814625 z - 412577550 z^2 + 76403250 z^3 - 4365900 z^4 + 93555 z^5 - 770 z^6 + 2 z^7) SinhIntegral[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]