Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7711)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-19/4

http://functions.wolfram.com/07.22.03.7711.01

Input Form

HypergeometricPFQ[{6}, {-(19/4), -(1/4)}, -z] == (1/15800400) (4 (3950100 - 19958400 z + 11710755 z^2 + 9442440 z^3 + 2363520 z^4 - 63488 z^5) + Sqrt[Pi] z^(5/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-25 (4385745 - 4733820 z - 3101616 z^2 - 806400 z^3 + 20480 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-109643625 - 27846000 z + 1428000 z^2 - 2688000 z^3 + 8192 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] z^(5/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-109643625 - 27846000 z + 1428000 z^2 - 2688000 z^3 + 8192 z^4) Cos[2 Sqrt[z]] + 25 (4385745 - 4733820 z - 3101616 z^2 - 806400 z^3 + 20480 z^4) 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]