Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a95r)

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=-11/4, b_1`>=-11/2

For fixed z and a₁=-11/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a95r.01

Input Form

HypergeometricPFQ[{-(11/4)}, {7/2, 13/4}, -z] == (1/(2433220608 z^(5/2))) (Sqrt[Pi] z^(1/4) (241215975 - 771891120 z + 2744501760 z^2 + 1125949440 z^3 + 75694080 z^4 + 1048576 z^5) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-70904295 + 120859200 z + 66178560 z^2 + 4669440 z^3 + 65536 z^4) Cos[2 Sqrt[z]] + 4 (21288960 - 61521075 z + 160110720 z^2 + 69511680 z^3 + 4718592 z^4 + 65536 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]