Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aby0)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.aby0.01

Input Form

HypergeometricPFQ[{3/4}, {-(11/2), 23/4}, -z] == -((1/(206158430208 z^(19/4))) (19 (1740375 Sqrt[Pi] (5030379585 + 523486656 z + 30868992 z^2 + 1425408 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (2918248956748125 - 1030368969630000 z + 94684330540800 z^2 - 2613262848000 z^3 + 17045651456 z^4) Cos[2 Sqrt[z]] + (-8754746870244375 + 8427333572658000 z - 1453579288761600 z^2 + 73378088448000 z^3 - 1056964608000 z^4 + 2147483648 z^5) Sin[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]